There are four circles in the figure. Two of them have radius 2 and the smallest one has radius 1. The radius of the largest circle, if the area of the dashed part is equal to the area of the dotted part, is __________
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The dashed part is the part of the three small circles outside the large circle, and the dotted part is the part of the large circle outside the three small circles. Adding the common overlap to both, equal areas mean the total area of the small circles equals the area of the large circle. So $$\pi R^2 = \pi(2^2 + 2^2 + 1^2) = 9\pi$$, and $$R = 3$$.